3. Consider the matrix=501-14 015(a) Find the eigenvalues of B and show that two eigenvalues are identical.(b) Determine all the eigenvectors of B.Hint: the double-eigenvalue determined in part (a) will only have one eigenvector.

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Answered: 3. Consider the matrix 5 B=0 4 1 1 1 0…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Q15
Help with b please
Consider the matrix 2 2 A = 4 2 2 (a) Compute the eigenvalues and eigenvectors of A. (b) Find rank one matrices B and C such that A = B + C and BC 0, explaining why the matrices you found have these properties. (hint: use your answer to part (a))
The matrix A := C = 12 -2 -3 13 has an eigenvector 6 (8) with eigenvalue 10. What is c?
4. Let -8 A = 1 1 Answer the following questions: (a) Find the eigenvalues, and bases for the eigenspaces. (b) Is A diagonalizable? If yes, find the matrix P that diagonalize A. Further, find A100.
Let B be a 3x3 matrix with eigenvalues 0,1,2. Then, the eigenvalues of BB T is (Hint: B and BT have the same eigenvalues) only 0 0,1,2 0,1,4 1,4
4. Find the eigenvalues for the matrix :) 1 -1 A = 1 2 1 -2 1 -1 For any one of these eigenvalues, find a specific corresponding eigenvector.
Let x = Express as a linear combination of 71, 72, and 73, and find Az. Az = -0--0-0 -1,72 = 3 be eigenvectors of the matrix A which correspond to the eigenvalues ₁-3, A₂ = -2, and A3 = 0, respectively, and let v₁+ V1 = √2+ ~2000 7 x = -5 -8 V3. = 4 2
Find all the eigenvalues (real and complex) of the matrix The eigenvalues are M = -9 12 3 -3 6 -2 -12 12 6 (Enter your answers as a comma separated list.)
9. Determine which of the following vectors 1 -1 is an eigenvector of the matrix 1 1 1 1 -1 1 -1 W = -1 -1 1 -1 -1 1 and find the corresponding eigenvalue.

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3. Consider the matrix 5 B=0 4 1 1 1 0 5 (a) Find the eigenvalues of B and show that two eigenvalues are identical. (b) Determine all the eigenvectors of B. Hint: the double-eigenvalue determined in part (a) will only have one eigenvector.